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P. Goodey, W. Weil. Centrally symmetric convex bodies and the spherical Radon transform. Journal of Differential Geometry, 1992, 35(3): 675-688.

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• 标题: 一般测度Busemann-Petty问题的稳定性Stability in the Busemann-Petty Problem for Arbitrary Measures

  作者: 汪卫

  关键字: Busemann-Petty问题, 星体, 凸体, Radon变换The Busemann-Petty Problem; Star Bodies; Convex Bodies; Radon Transform

  期刊名称: 《Pure Mathematics》, Vol.2 No.4, 2012-11-01

  摘要: 基于Zvavitch将Busemann-Petty问题推广到了一般测度，本文利用Radon变换研究了一般测度Busemann-Petty问题的稳定性。作为应用，我们建立了n(n≤4)维空间中的一个关于一般测度的超截面不等式。这些结果与Koldobsky利用Fourier变换证明的结论是一致的。 Zvavitch found a generalization of the Busemann-Petty problem to arbitrary measures. In this paper, we study the stability in the Busemann-Petty problem for arbitrary measures by using Radon transform. As application, we obtain a hyperplane inequality for arbitrary measures in dimensions up to four. These results are consistent with Koldobsky’s results which are obtained by using Fourier transform.